Sumudu transform iteration method for fractional diffusion-wave equations by Khosro Sayevand, Kazem Pichaghchi

“…In this article, we have implemented Sumudu transform iteration method as a new approximate analytical technique for solving fractional diffusion-wave equations. …”
Get full text

Solve Schrodinger Fractional Order Boundary Value Problem by Laplace Transformation Method by Shwan Fatah, Hozan Hilmi, Karwan Jwamer

“…We proved the solution using the Laplace transformation after obtaining the existence using the fractional integral and integral operator methods.…”
Get full text

Comparative Study of the Nonlinear Fractional Generalized Burger-Fisher Equations Using the Homotopy Perturbation Transform Method and New Iterative Transform Method by Mashael M. AlBaidani

“…We compare the homotopy perturbation transform method and the new iterative method in the current study. …”
Get full text

Solving Nonlinear Fractional Partial Differential Equations Using the Elzaki Transform Method and the Homotopy Perturbation Method by Mohamed. Z. Mohamed, Mohammed Yousif, Amjad E. Hamza

“…To obtain the solution to an equation, we use the inverse transforms of the Elzaki transform method (ETM). The initial conditions have a big impact on the equation’s result. …”
Get full text

Solving Nonlinear Fractional Models in Superconductivity Using the q-Homotopy Analysis Transform Method by Khalid K. Ali, M. Maneea, Mohamed S. Mohamed

“…This study describes the q-homotopy analysis transform method (q-HATM) as a powerful technique for solving nonlinear problems, which has been successfully used with a set of mathematical models in physics, engineering, and biology. …”
Get full text

A comparative study on residual power series method and differential transform method through the time-fractional telegraph equation by Devshali Pratiksha, Singh Prince

“…This work investigates, applies, and compares two semi analytical methods, namely, reduced fractional differential transform method and the Laplace-transformed residual power series method, toward solving the two-dimensional time-fractional telegraph equation. …”
Get full text

A Comprehensive Study on the Applications of NTIM and OAFM in Analyzing Fractional Navier–Stokes Equations by Siddiq Ur Rehman, Rashid Nawaz, Faisal Zia, Nick Fewster-Young

“…This article introduces two enhanced techniques: the Natural Transform Iterative Method (NTIM) and the Optimal Auxiliary Function Method (OAFM). …”
Get full text

Analytical Insight into Some Fractional Nonlinear Dynamical Systems Involving the Caputo Fractional Derivative Operator by Mashael M. AlBaidani

“…This study develops the new iterative transform technique (NITM) and homotopy perturbation transform method (HPTM) using Elzaki transform (ET) with a new iteration method and a homotopy perturbation method. …”
Get full text

Local fractional Elzaki transform and its application to local fractional differential equations by Mountassir Hamdi Cherif, Djelloul Ziane

“…The objective of our work is to couple the Elzaki transform method and the local fractional derivative which is called local fractional Elzaki transform, where we have provided important results of this transformation as local fractional Laplace-Elzaki duality, Elzaki transform of the local fractional derivative and the local fractional integral and the local fractional convolution, also we have presented the properties of some special functions with the local fractional derivative sense. …”
Get full text

The series solutions of fractional foam drainage and fractional modified regularized long wave problems by Abdul Hamid Ganie, N. S. Alharthi, Adnan Khan, Abdulkafi Mohammed Saeed, Mohd Asif Shah, Saurav Mallik

“…In this work, we offer two novel techniques by combining the Elzaki transform with the Adomian decomposition method (ADM) and the homotopy perturbation method (HPM). …”
Get full text

Analytical Analysis of Fractional-Order Newell-Whitehead-Segel Equation: A Modified Homotopy Perturbation Transform Method by Naveed Iqbal, Abeer M. Albalahi, Mohammed S. Abdo, Wael W. Mohammed

“…This paper has applied a hybrid method called the homotopy perturbation transformation technique to solve fractional-order Newell-Whitehead-Segel equations. …”
Get full text

Wave solution for time fractional geophysical KdV equation in uncertain environment by Mrutyunjaya Sahoo, Dhabaleswar Mohapatra, S. Chakraverty

“…To deal with such uncertainty, this work aims to find the approximate fuzzy solution to the said physical problem by applying a double parametric approach with the help of an effective method called the fractional reduced differential transform method (FRDTM). …”
Get full text

An Approximate-Analytical Solution to Analyze Fractional View of Telegraph Equations by Izaz Ali, Hassan Khan, Umar Farooq, Dumitru Baleanu, Poom Kumam, Muhammad Arif

“…The Caputo-operator is used to express the derivative of fractional-order. The present method is the combination of two well-known methods namely Mohan transformation method and Adomian decomposition method. …”
Get full text

Application of Triple- and Quadruple-Generalized Laplace Transform to (2+1)- and (3+1)-Dimensional Time-Fractional Navier–Stokes Equation by Hassan Eltayeb Gadain, Said Mesloub

“…In this study, the solution of the (2+1)- and (3+1)-dimensional system of the time-fractional Navier–Stokes equations is gained by utilizing the triple-generalized Laplace transform decomposition method (TGLTDM) and quadruple-generalized Laplace transform decomposition method (FGLTDM). …”
Get full text

Gas well productivity prediction based on fractional Fourier transform by Chenchang Zheng, Jun Tang, Mengfan Li, Gewei Qi

“…In order to solve this problem, this paper uses relatively low cost logging data to investigate the relationship between Stoneley wave, longitudinal and transverse wave sign and reservoir characteristics. Fractional Fourier transform is introduced to improve signal processing methods and extract key parameters, including Stoneley wave frequency offset rate and energy attenuation coefficient of longitudinal and transverse wave. …”
Get full text

Analysis of Time-Fractional Delay Partial Differential Equations Using a Local Radial Basis Function Method by Kamran, Kalsoom Athar, Zareen A. Khan, Salma Haque, Nabil Mlaiki

Get full text

W transform and its application in fractional linear systems with rational powers by Guishu Liang, Mingjue Jiang

“…When this transformation is applied to fractional linear systems with rational powers, the expansion formula will have a large number of terms if the traditional decomposition method is used, which makes the form of time‐domain solutions more complex. …”
Get full text

Investigating the truncated fractional telegraph equation in engineering: Solitary wave solutions, chaotic and sensitivity analysis by Usman Younas, Jan Muhammad, Muhammad Amin S. Murad, D.K. Almutairi, Aziz Khan, Thabet Abdeljawad

“…For this purpose, the Galilean transformation is applied, and a variety of graphs in 2D phase portraits and time-series analyses have been sketched. …”
Get full text

Iterative procedure for non-linear fractional integro-differential equations via Daftardar–Jafari polynomials by Qasim Khan, Anthony Suen

“…In this paper, we introduce a novel approach called the Iterative Aboodh Transform Method (IATM) which utilizes Daftardar–Jafari polynomials for solving non-linear problems. …”
Get full text

Solution of Fractional Partial Differential Equations Using Fractional Power Series Method by Asif Iqbal Ali, Muhammad Kalim, Adnan Khan

“…Noninteger derivatives are considered in the Caputo operator. The fractional-order power series technique for finding the nonlinear fractional-order partial differential equation is found to be relatively simple in implementation with an application of the direct power series method. …”
Get full text